[tinypass]

Tinypass does exactly this with its "Counter" feature that displays to readers how many free previews they have left in the metered paywall. Then, when the meter expires, the content is blocked or a donation is requested. Hundreds of publishers are using the platform. http://tinypass.com

[prawn]

Something like that but without the barrier/limit that stops people from continuing to browse the site.

With Tinypass: hits limit of 10 articles, donation of $5 requested; non-payers go elsewhere for their content

With my hypothetical: user ignores donation at 10 articles, maybe gets to 100. Isn't going to a competitor for content. Potentially decides that 100 articles seems like a lot, surely that's worth at least $5.